Express the following with positive indices

3 and p to the power of -2 and q

divide by r to the power of -3

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To express in positive indices:

3 and p to the power of -2 and q

divide by r to the power of -3.

Solution:

'and' is taken as mulplication.

The given expression words becomes

(3 and p to the power of -2 and q)/r to the power of -3

(3p^(-2q))/(r^(-3).

Now we use a^(-b) = 1/a^b.

Therefore (3p^(-2q))/(r^(-3)) = (3/P^(2q))/ (1/r^3)

(3/p^(2q))/(1/r^3) = 3r^3/p^(2q)

Therefore {3p^(-2q) }/r^(-3) = 3r^3/p^(2q) in which all the powers p and q are in positive form.

We have to express the following as terms with positive indices :

3 and p to the power of -2 and q divide by r to the power of -3

=> (3 + p)^(-2 + q) / r^(-3)

reverse the power of r and bring it to the numerator

=> [(3 + p)^(-2 + q)] * r^3

=> [(3 + p)^( q - 2)] * r^3

There is nothing more that can be done here as neither the bases or the powers of the terms are the same.

**Therefore the required result is [(3 + p)^(q - 2)] * r^3**

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